You can use your cement board to end where you want and just use some sheet membrane out to the area the tiles extend. I myself don't care for cement board as it's not waterproof at all. But use Laticrete Hydroban board and sheet membrane on the edge and or Schluter and Mapei now makes waterproof board also. Much easier to work with. Not a fan of the Schluter but to each his own. Look up Sal Diblasi on U tube https://www.youtube.com/watch?v=V8_EvJa3SYE and his latest video shows what to do with that area your worried about.

Wow, big gap, I wonder why it was done like that. I suggest the backer rod then fill the shower full of water with the drain covered to weigh it down. Then use 100% neutral curing silicone. If it's just white GE makes one that is guaranteed to not mold. I have used it and it's very good. I believe it's call Supreme. Just make sure you us a Neutral curing silicone. You can get it color matched through Mapei, Laticrete etc.

Most big box stores will carry it. Do not use caulk or Siliconized caulk. On all change of planes you must use 100% silicone. Caulk is just gonna crack. Use a smoothing tool to put the silicone in and a spray bottle with water and a couple of drops of Dawn. It will give you professional results. Once put on give it a long time to cure as that is one huge gap. Then drain the water and you should be good to go.

Back in the Early 2000's I bought a built in 1994 house in Florida that was all glued down sheet vinyl on concrete. I wanted to tile it and ripped up this ugly black and white vinyl. But the glue would not come off easily. Now mind you it was over 2000 square feet. Scraping it did nothing and I was at my wit's end. So someone had recommended a grinder also but just before we were heading to rent one I had a 5 gallon bucket full of water that I accidentally knocked over and got a good portion of the glue wet. After a little bit of time my friend took a scraper and low and behold the glue just came up.

Once we figured out it was water based glue we were able to remove the glue with no fuss at all with a big scraper. Saving a big mess with a grinder. You may want to see if the glue is water based by putting some water on it and wait a bit. I still live in the house and the tile is holding up great. Oh, btw why do you want to put ditra on a concrete floor? I don't see a need in that unless maybe your heating it.